Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets
Classical Analysis and ODEs
2015-02-18 v3
Abstract
Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint time-frequency analysis is introduced. It is shown that any Fourier eigenfunction achieve isoresolution. It is shown that an isoresolution wavelet can be derived from each known wavelet family by a suitable scaling.
Cite
@article{arxiv.1502.03401,
title = {Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets},
author = {L. R. Soares and H. M. de Oliveira and R. J. Cintra and R. M. Campello de Souza},
journal= {arXiv preprint arXiv:1502.03401},
year = {2015}
}
Comments
6 pages, XX Simp\'osio Bras. de Telecomunica\c{c}\~oes, Rio de Janeiro, Brazil, 2003. Fixed typos